Use Properties of Use Properties of Trapezoids and KitesTrapezoids and KitesChapter 8.5

TrapezoidsTrapezoidsTrapezoids are quadrilaterals

that have 2 parallel sidesThe parallel sides are called the

bases.◦A trapezoid has 1 pair of base

angles.The non-parallel sides are called

the legs.base

baseLeg Leg

Is it a trapezoid?Is it a trapezoid?Are the bases parallel?

Find the slope of each base.

If the slopes are the same, then it is a trapezoid.

Isosceles TrapezoidsIsosceles TrapezoidsIsosceles triangles have 2

congruent sides with 2 pairs of congruent angles.

The diagonals of an isosceles trapezoid are also congruent.

If it is Isosceles find the If it is Isosceles find the missing angles.missing angles.

It is isosceles!

Because it is an isosceles trapezoid, the base angles are congruent.Therefore m <A = m <B, and m <D = m <C

53º

Angle A and Angle D are supplementary.180 – 53 = 127

127º

127º

Find the missing angles if it Find the missing angles if it is an Isosceles Trapezoid.is an Isosceles Trapezoid.

97º

83º

83º

MidsegmentsMidsegmentsA midsegment is a segment that

connects 2 midpoints.

The midsegment of a trapezoid connects the midpoints of the legs.

Find the length of the Find the length of the midsegmentmidsegment

)(2

1GFDEHK

)186(2

1HK

12HK

Things always have to be Things always have to be more difficultmore difficult

)(2

121 basebasemigsegment

)3527(2

15.19 x

)530(2

15.19 x

x5.2155.19 x5.25.4 x8.1

19.5

5x + 3

Find xFind x)(

2

121 basebasemigsegment

)151045(2

15.52 x

)1060(2

15.52 x

x5305.52 x55.22 x5.4

52.5

45

10x + 15

Page 546, #3 – 15, 25 - 27Page 546, #3 – 15, 25 - 27

KitesKitesA kite is a quadrilateral with 2

pairs of congruent sides, but the opposite sides are not congruent.

DiagonalsDiagonals If the diagonals of a kite are perpendicular, then what shape is created by the diagonals?If we are given these side lengths, can we find the missing sides XY, WX, YZ , and WZ?

222 cba 222 33 XY299 XY

218 XY218 XY

WXXY 23

222 53 YZ2259 XY

234 XY234 XY

WZYZ 34

Find XY, ZY, WX, and WZFind XY, ZY, WX, and WZ

222 126 XY214436 XY

2180 XY2180 XYZYXY 56222 64 WX

23616 WX252 WX252 WX WZWX 132

6√52√13

Find XY, YZ, WZ, and WXFind XY, YZ, WZ, and WX222 510 XY225100 XY

2125 XY2125 XYYZXY 55

222 1910 WZ2361100 WZ

2461 WZ2461 WZWXWZ 461

5√5

√461

The figure below is a kite, The figure below is a kite, find the missing anglesfind the missing angles

What is the sum of the interior angles of a kite? 360

100 + 40 + mó E + mó G = 360 140 + mó E + mó G =

360mó E + mó G = 220What do we know about the measures of

the angles E and G?They are congruent!

1102

220

Find the missing anglesFind the missing angles

60 + 110 + 110 + mó G = 360

What do we know about the measures of the angles F and H?They are

congruent!110º

280 + mó G = 360mó G =

80

80º

Find the missing anglesFind the missing angles

150 + 90 + mó F + mó G = 360

240 + mó F + mó G = 360mó F + mó G =

120mó F = mó G

602

120